For me, it would be my 7mm-08. Large enough for bear, and great for deer. I figure I could still use it for coyotes but would probably use my shotgun allot more.
Can I take one rifle with multiple barrels like an Encore?
In all seriousness, I'd probably choose a .243 Winchester. I don't tend to hunt really big game all too often, so it would work out pretty well for me. If I was thinking that I was going to hunt elk or bear, I'd probably opt for a .270 Winchester or .30-06 Springfield.
Thought I'd say it before somebody else did 8P~
On a serious note, living in Hoosier-land, I'd give a 22lr a really hard look. About 90% of the critters around here are legitimate rimfire fodder.
If we are talking "Hunting Rifle," here in Wyoming it would have to be my Ruger 77 RS FB 6mm. Burris 3X-9X 40mm BP. Certainly a stretch for a Big Bull Elk and overkill on the Prairie Dogs. But a good compromise for me.
However if/when the SHTF I would sure miss my AR! Hmmm, perhaps I need an AR 10 .243.
Probably my combo gun in 12ga/223. Then I can have my one rifle and 1 shotgun at the same time. Between reloading and the various 12ga loads out there, I can hunt anything in North America with it and probably live to tell about it. Wide variety from shot sizes to 30 gr. Bergers and 500gr.+ slugs.